Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

Abstract

We develop a systematic variational coherent state expansion for the many-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counterdisplacements due to quantum tunneling effects). We present a comprehensive study of the ground state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization group calculations and to the exact Bethe Ansatz solution of the model demonstrate the rapid convergence of our variationally-optimized multi-polaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.

Polaron dynamics with a multitude of Davydov D2 trial states

“…Very recently, a systematic coherent-state expansion of the ground state wave function that is based on the Davydov D 1 Ansatz, which we shall call the "multi-D 1 Ansatz," is developed for a number of models [59][60][61]. It is a generalization of a variational wave function originally proposed by Silbey and Harris [62], and also an extension of the hierarchy of translationlly-invariant Ansätze proposed by Zhao et al [48,49] A jnq…”

The asymmetric quantum Rabi model in the polaron picture

“…This resembles the polaron in condensed matter, where the electron is surrounded with photons that are induced by deviation of atoms from their equilibrium positions. Thus, these right (x 0 ) and left (−x 0 ) displaced states can be considered as polarons [17,18,55]. The polaron located at x 0 is bounded to |− z and that located at −x 0 is bounded to |+ z .…”

“…[9]) but also in a variety of other fields such as, for example, BoseEinstein condensation [10,11], nanoscience [12], biophysics [13], polymers [14][15][16], and so on. Recently, it has also been extended to study spin coherence [17,18] in a dissipative quantum system, namely, the spin-boson model [19,20]. While these works [17,18] have focused on the dissipative environment, the physics of polarons in a single-mode optical field have not been explored systematically.…”

“…Recently, it has also been extended to study spin coherence [17,18] in a dissipative quantum system, namely, the spin-boson model [19,20]. While these works [17,18] have focused on the dissipative environment, the physics of polarons in a single-mode optical field have not been explored systematically. In fact, a two-level atom (qubit) coupled to a single-mode optical field is the simplest system describing the interaction between light and matter, which is a basic model in quantum optics [21,22], quantum information [23], and condensed matter physics [24].…”

Dynamics of a qubit in a high-impedance transmission line from a bath perspective

“…In addition, a brute force Fock truncation of the full Hilbert space becomes numerically prohibitive due to the large number of photons generated in the environment, unless one can target physical states using an optimal variational basis, such as matrix product states (MPS) [16][17][18][19][20] or within the systematic coherent state expansion (CSE) pioneered in Ref. 21 and susequently extended to a variety of dissipative models [22][23][24][25].…”